Health and Retirement Effects in a Collective
Consumption Model of Older Households
Aline Bütikofer Arthur Lewbel Shannon Seitz
University of Bern Boston College Boston College
January 2011
Abstract
Using data on older individuals and couples, we estimate a collective model of household
consumption of a variety of goods, showing how resources are shared between husbands and
wives, and how this allocation is affected by retirement and health status. We identify the extent
to which shared consumption of goods by older married couples reduces their costs of living
together relative to living alone. We also identify the fraction of household resources consumed
by wives versus husbands, taking the jointness of some consumption into account. The results
are relevant for household bargaining models and for a variety of welfare calculations.
Among other results, we nd that older couples save between 24 and 40 percent on expenditures by sharing consumption of goods, that older wives consume between 30% and 42% of
total household expenditures (taking sharing of goods into account), and that these shares are
little affected by retirement, but increase dramatically when the husband's health is poorer.
JEL codes: D13, D12, I1, D6, C30
Keywords: Collective household models, Bargaining models, Retirement, Aging, Health, Equivalence scales, Indifference scales, Cost of Living, The Elderly, Consumption, Welfare.
This research was supported in part by the Steven H. Sandell Grant Program, Center for Retirement Research, Boston College. Corresponding Author: Arthur Lewbel, Department of Economics, Boston College,
140 Commonwealth Ave., Chestnut Hill, MA, 02467, USA. (617)-552-3678, lewbel@bc.edu,
http://www2.bc.edu/arthur-lewbel/
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1 Introduction
Much public policy and research is focused on the living standards of the elderly, a group of
particular concern because of the unique set of circumstances they face, including: (1) retirement
and the decline in income that is typically associated with retirement, (2) declines in health status
and increases in unanticipated medical expenses, and (3) illness and/or the death of a spouse.
The goal of this paper is to apply recent advances in the modelling of collective household
behavior to the speci cs of older households. In particular, we assess the living standards of individuals within households, and determine how those standards of living change with retirement,
illness, and widowhood.
For an individual living alone, the link between consumption expenditures and attained standard of living is immediate; indeed, the latter is generally de ned in terms of the former. But
for a household, the connection is complicated by three factors: differences in preferences across
household members, economies of scale in consumption, and the resource allocation across household members. By jointly consuming some goods (e.g., home heating or traveling together in the
family car), a two member household can attain a higher standard of living for its members than
two individuals living alone with the same total income or expenditure level. Evaluating the standard of living of individuals within households therefore requires estimating the extent to which
consumption goods and services are jointly consumed.
The standard of living within a household also depends on how the household's resources are
allocated among household members. Previous work by Lise and Seitz (2011) using UK expenditure data highlights the fact that consumption inequality within households may be substantial:
ignoring within household inequality underestimates the level of cross sectional consumption inequality by 30 percent, as large differences in the earnings of husbands and wives translate into
large differences in consumption allocations within households.
Household bargaining models suggest allocations will depend at least in part on the relative
incomes of husbands and wives (e.g. Becker, 1965, 1981). Since relative incomes generally change
abruptly at retirement, one of our goals is to see how household resource shares change with
retirement. The absolute and relative health of household members could also have a substantial
impact on both the preferences and bargaining power of household members, and these effects are
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likely to be particularly important in older households.
The type of model we employ assumes a collective household that is characterised as a set of
individuals, each of whom has a well de ned objective function and interacts to generate household level decisions. We use the type of model in which household level consumption data are
used to recover information about individual household members. Examples include Chiappori
(1988, 1992), Bourguignon and Chiappori (1994), Browning, Bourguignon, Chiappori, and Lechene (1994), Browning and Chiappori (1998), Vermeulen (2002), Browning, Chiappori and Lewbel
(2004), Lise and Seitz (2011), and Cherchye, De Rock, and Vermeulen (2008). These models are
very useful because our available data on consumption decisions of older couples only contains
consumption information on household level choices, while the objects of interest are based on the
preferences of, and constraints faced by, the individuals who together make up the household.
Our speci c analysis uses the model of Lewbel and Pendakur (2008) (which is in turn a simpli ed version of Browning, Chiappori and Lewbel 2004), suitably augmented to contain variables
associated with health, retirement, and other attributes of older households. The advantages of this
model for our application are that it has less intense data requirements (particularly regarding price
data) relative to most other models in this literature, and it delivers estimates of the resource shares
and relative standards of living that are the goal of our analysis. Our results extend these earlier
collective model papers in directions of particular importance to the study of retirement and aging,
and in particular we focus on the roles of health status and retirement.
Declines in health status are an inevitable part of the aging process and interact in important
ways with household consumption behavior. Previous research indicates that out-of-pocket medical expenses can be substantial, even for those with health insurance (French and Jones, 2004;
Feenberg and Skinner, 1994; Palumbo, 1999). Palumbo (1999) estimates that roughly 10% of
older households spend 20% or more of their income on out-of-pocket medical expenses, not including nursing home expenditures. We allow health status to affect both economies of scale in
consumption as well as the allocation of resources between husbands and wives.
Evidence from previous research indicates that expenditure patterns tend to change at retirement and that retirement is a household and not an individual decision (Banks, Blundell, and
Casanova Rivas, 2007; Blau, 1998; Blau and Gilleskie, 2006; Gustman and Steinmeier, 2000;
Hurd, 1990; Michaud and Vermeulen, 2004). In this paper we allow age and retirement to affect
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the allocation of resources (potentially via bargaining power) and jointness of consumption in two
person households.
A limitation of our empirical model is that it is static, and so does not measure dynamic and
forward looking implications of retirement and health declines on welfare and consumption allocations. Our results condition on health and retirement status at the moment, and so cannot be used
address issues such as when individuals within households choose to retire, or how they choose to
allocate their savings over time. We assume a time separable model and focus on the allocation
of household's consumption expenditures within a time period, rather than over time. This simpli cation allows us to make use of cross section or short panel data while still addressing many
fundamental questions of interest.
Using our model, the types of questions we address in this analysis are: To what extent does
joint consumption increase following retirement or changes in the health status of one or both
spouses? How does the allocation of resources to husbands versus wives change with illness and
retirement? What are the costs of maintaining a xed standard of living when a spouse dies?
Many policy and welfare calculations depend on answering these questions correctly. These results
should be useful for constructing poverty lines for the older, for determining appropriate levels of
social and private insurance, for indexing welfare, pension, or social security payments, and for
calculating appropriate measures of welfare inequality in the older population.
2 Data Summary
The data consist of characteristics of one and two person households around the age of retirement
in the US Health and Retirement Study (HRS) and a supplement to the HRS, the Consumption
and Activities Mail Survey (CAMS). The HRS contains demographic information, comprehensive
information on retirement and health status, as well as detailed income data. The CAMS contains
data on total annual household expenditures as well as expenditure data for a set of 38 consumption
goods and data on 33 different activities.
For the purposes of this paper, we use data from the 2005 and 2007 waves of the HRS/CAMS.
The sample is restricted to married couples and widows/widowers between the ages of 50 and 80.
We also exclude households in the bottom and top 5 percent of the total expenditure distribution.
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Our remaining sample consists of 1004 married couples, 420 widows and 79 widowers. The demographic characteristics are summarized in Table 1. Relative to one person households, married
couples are much more likely to be college educated and in good health. Widows tend to be older
and are more likely to be retired than singles and married couples.
We consider 10 expenditure categories: groceries, restaurant meals, gasoline, personal care,
clothing, vacation, utilities, garden supplies and services, car maintenance, and housing (home
repairs, supplies and services). In Table 2 we rst document the distribution of expenditures across
household type. Interesting expenditure patterns across gender emerge from the data: women tend
to spend more on clothing, gardening and personal care while men tend to have higher expenditures
on restaurant meals and gasoline.
Married couples and widows appear to devote a larger share of their budgets to groceries and
home maintenance. As expected, married couples in particular spend more on vacations and less
on utilities relative to single person households. In Table 3, we consider how budget shares for
married couples differ conditional on the retirement status of each spouse. In general, expenditures
on items related to work or transportation (restaurant meals, gasoline, personal care, clothing,
car maintenance) tend to be higher in households where at least one spouse is not retired and
expenditures related to home production (groceries, gardening) and leisure (vacations) tend to be
higher in households in which at least one spouse is retired.
Finally, consider the way budget shares vary with health status in married couples. We use
qualitative information on self-reported health to measure health status in our empirical exercise.
The HRS contains the following question “Would you say your health is excellent, very good, good,
fair, or poor?” which will be used to construct our preliminary measure of health status. This or
similar measures have been used in previous studies (Palumbo, 1999; De Nardi, French, and Jones,
2006). Wallace and Herzog (1995) provide a comprehensive review of the health information
available in the HRS. In Table 4 we document the distribution of expenditures in married couples
by the health status of each spouse. In general households devote a higher share of expenditures to
groceries, gasoline and utilities and a lower share to restaurants and vacations when either spouse
is in poor health, suggesting spouses may be spending more time at home. When the husband is
in poor health, households tend to spend slightly more on personal care and clothing (goods that
single women tend to spend relatively more on) and when the wife is in poor health households
5
tend to spend more on car maintenance (a good single men tend to spend relatively more on).
3 Resource Shares and Indifference Scales
Two attributes of collective households that we will be identifying and estimating are resource
shares and indifference scales, as de ned in Browning, Chiappori, and Lewbel (2004). For a
couple, let q f and qm be consumption bundles, i.e., K vectors of quantities of goods and services
consumed by the wife and by the husband respectively. If market prices of the goods and services
are given by the K vector p, then de ne the wife's resource share
so the resource share
fraction 1
by
D p 0 q f = p 0 q f C p 0 qm ,
is the fraction of total resources that are devoted to the wife, with the
being the husband's resource share.
As will be discussed more fully in the next section, the total bundle q of goods and services
purchased by the household will in general be smaller than (rather equal to) q f Cqm , because some
goods may be consumed jointly, resulting in economies of scale in consumption. In particular, for
goods that are publicly consumed within the household, like heat, the quantity consumed can
equal up to twice the amount purchased, since each household member can consume up to the
total amount purchased. Let total household expenditures be x D p 0 q. Because of jointness
of consumption x can be less than, rather than equal to p 0 q f C p 0 qm . For internal consistency,
resource shares are de ned in terms of fractions of the latter, rather than as fractions of x. We
will be interested in estimating these resource shares as measures of inequality within a household.
Browning, Chiappori, and Lewbel (2004) show that, using this de nition, resource shares are
monotonically increasing in Pareto weights, and so in bargaining models
can be interpreted as a
measure of the relative bargaining power of the wife.
Unlike resource shares, which compare the wife to the husband, indifference scales are welfare
measures that compare the same individual in two different situations; living alone versus with a
spouse. An indifference scale I j of an individual j is de ned as follows.
First consider a woman living with a husband, where the couple has a total expenditure level y
and faces prices p. She consumes the bundle q f , which is determined by some household decision
making process, and so attains a utility level U f q f , where U f is her utility level over goods.
Note that q f will depend in part on her resource share within the household, and on the extent
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to which consumption in the household is joint. Now suppose she lived alone instead of with a
spouse. Let y j be the total expenditure level she would require at prices p to buy a bundle e
qf
that gives her the same utility as q f , so U f q f D U f e
q f . Then her indifference scale (at total
expenditure level y and prices p) is de ned as I f D y j =y.
In short the indifference scale I f is the fraction of the couple's income y that she would need, if
living alone, to attain the same level of utility from consumption that she obtains from living with
a partner. Indifference scales differ from ordinary adult equivalence scales (see Lewbel 1997 for a
survey) in that equivalence scales equate the utility of an individual to the utility of a household,
and so suffer from fundamental identi cation problems associated with interpersonal comparisons
of utility. In contrast, indifference scales are invariant to how utility is cardinalized. Speci cally,
replacing U f q f with any monotonic transformation of her utility function leaves the indifference
scale unchanged.
As a result, unlike equivalence scales, indifference scales can at least potentially be identi ed
just from revealed preference data. Intuitively, the reason for this difference is that equivalence
scales compare the utility of two different entities, namely, an individual and a household. In
contrast, indifference scales compare the same individual in two different settings, i.e., living alone
facing market prices, versus living in a household, consuming his/her share of the household's
resources and facing shadow prices.
Indifference scales are particularly well suited for assessing the welfare impacts of widowhood,
since they describe exactly in percentage terms how much income the surviving wife can afford to
lose as a result of the spouse's death, without a reduction in her standard of living.
4 The Model
We apply the model of Lewbel and Pendakur (2008), which is itself a restricted version of the
household consumption model of Browning, Chiappori and Lewbel (2004). This restriction permits the use of cross section data without price variation, of the type we have available in the
HRS.
In our application of their model, consider households of three types: single women (speci cally widows), single widower men, and married older couples. Index the members of the house7
hold by j D f (female) and j D m (male). Let z j denote a vector of observed demographic
characteristics for each individual, which includes their health and retirement status, among other
attributes. The individual has a utility function U j q; z j , which denotes the utility he or she gets
from consuming a bundle (a K vector) of quantities of goods q. Individuals are assumed to all be
facing the same vector of prices p for goods and services.
Consider the behavior of singles rst. An individual j having total expenditures y will choose
to consume a bundle q j p; z j obtained by maximizing U j q j ; z j subject to the budget constraint
PK
y D p 0 q j D kD1
p k q kj . Let w kj y; z j D p k q k p; z j =y denote the resulting fraction of total
expenditures y that the individual spends on good k, so wkj is a budget share. Since all consumers
face the same prices, p is a constant that we have dropped from wkj y; z j . The function wkj y; z j
is therefore a budget share Engel curve, that is, a Marshallian demand function, in budget share
form, evaluated at a xed price vector.
Now consider couples. A couple or household h consists of two individuals, having utility
functions U f and Um respectively. In addition to the attributes z f and z m of its members, the
household h may be characterized by an additional vector of household attributes z h . These z h
may affect how the household allocates resources among its members. A household h is also
assumed to have a diagonal K by K matrix Ah that summarizes the extent to which each good can
be jointly consumed. The element Akh in the k 0 th row and column of Ah is the Barten (1964) scale
for good k. The idea is that a household that purchases a quantity q k of good k can act as if it had
actually purchased the quantity q k =Akh of the good, and so the wife can consume a quantity q kf and
husband a quantity qmk , where q kf C qmk D q k =Akh . Each Akh is a number between one half and one,
where the closer the number is one, the less the good is jointly consumed. A purely private good
k would have k D 1. In the full Browning, Chiappori and Lewbel (2004) model, price variation
is exploited to estimate these Barten scales along with the rest of the model. In our cross section
framework we will only be able to identify some useful summary measures of economies of scale
in consumption, but not the individual Akh parameters.
The couple chooses consumption quantities q f and qm to maximize
V U f q f ; z f ; Um .qm ; z m / ; p; y; z h ;
where V may be a social welfare function, or bargaining function, or any other function that is
8
strictly increasing in U f and Um and so yields a Pareto ef cient allocation of resources within the
household. In addition to depending on the utility of household members, V may also directly
depend on variables like z h . So, e.g., in a bargaining model z h could include the relative wages of
the husband and wife, which could in turn affect the allocation of resources within the household
through the function V .
The household having total expenditures y chooses a purchased quantity vector q and associated consumption quantity vectors q kf and qmk to maximize V subject to the consumption technology (economies of scale) constraint q f C qm D Ah 1 q and the budget constraint p 0 q D y. Lewbel
and Pendakur (2008) show that, given some restrictions on the function V , couples will choose to
purchase budget shares given by
whk .y; z/ D .z/ w kf
.z/ y
;zf
f zf
!
C [1
k
.z/] wm
[1
.z/] y
; zm
m .z m /
for each good k, where z is the union of the elements of the vectors z f , z m , and z h ,
.z/ is the
fraction of the household's resources (total expenditures) that are allocated to the wife, and
and
m
f
zf
.z m / are functions associated with the economies of scale associated with joint consumption
in the household. Note that both .z/ and
j
.z/ implicitly depend upon Ah and p. In this model,
Lewbel and Pendakur (2008) show that indifference scales are given by I f .z/ D
and Im .z/ D
m
.z m / = [1
f
z f = .z/
.z/]. These indifference scales embody both the economies of scale
and resource allocations associated with being married versus single.
A key identifying assumption in the Lewbel and Pendakur (2008) and Browning, Chiappori
and Lewbel (2004) model is that the utility functions U f and Um , denoting the tastes of women
and men, are the same whether they live alone or in couples, so that the differences in purchasing
patterns between singles and couples are entirely due to jointness of consumption of some goods
(economies of scale to consumption) and to resource allocations between husband and wife. This
restriction can be relaxed in these models by observing expenditure allocations across goods within
households, or by functional form restrictions on any utility changes that occur with marriage.
However, in the present context we deal with this issue by restricting attention to singles who are
widows or widowers. Unlike people who are single by choice, those individuals chose to marry,
and so presumably have the same tastes on average as married individuals.
Following Lewbel and Pendakur (2008), we choose functional forms for utility that yield bud9
get shares for singles w kj y; z j of the form
k0
w kf D a k0
f C a f z f C ln y
e0f z f bkf C ln y
e0f z f
k
wm
D amk0 C amk0 z m C ln y
0
k
em
z m bm
C ln y
0
em
zm
2
ckf C " kf
(1)
for women and
2 k
cm
C "km
(2)
k
k
for men, for each good k D 1; :::; K . Here the parameters a k0
j , b j , and c j are scalar constants to
be estimated (using data from widows and widowers) for each good k and gender j, while a kj and
e j are constant parameter vectors to be estimated. The constraint that budget shares sum to one
PK
PK
PK k
PK
k
k
imposes the restrictions that, for each j, kD1
a k0
D
1,
b
D
0,
c
D
0,
and
kD1 j
kD1 j
kD1 a j
j
equals a vector of zeros.
These budget shares correspond to a rank three demand system (see Lewbel 1997) that is
quadratic in log total expenditures, which many authors have found provide a good t for Engel
curves (see, e.g., Banks, Blundell, and Lewbel 1997), and are a quadratic in demographic characteristics that is restricted to satisfy shape invariance, which is also known to t well empirically
(see, e.g., Blundell, Duncan and Pendakur 1998).
For couples, we again follow Lewbel and Pendakur (2008) and specify the resource sharing
rule .z/ and the log of the economies of scale functions
j
z j as linear in z, so
.z/ D r 0 z D r0 C rh0 z h C rm0 z m C r 0f z f
(3)
and
ln
j
z j D d0 j C d 0j z j
(4)
for j D f; m, where r0 , d0 f , and d0m are constant scalar parameters and d f , dm , rh , rm , and r f
are constant parameter vectors. Pulling together these expressions yields budget share demand
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functions for couples having the functional form
whk D
k0
r 0 z .a k0
f C af zf
(5)
C ln y C ln r 0 z
d0 f
d 0f z f
e0f z f bkf
C ln y C ln r 0 z
d0 f
d 0f z f
e0f z f
2
ckf /
r 0 z .amk0 C amk0 z m
C 1
C ln y
ln 1
r 0z
d0m
dm0 z m
k
0
z m bm
em
C ln y
ln 1
r 0z
d0m
dm0 z m
0
em
zm
2 k
cm / C "kh
for k D 1; :::; K . These also imply functional forms for the indifference scales given by
ln I f .z/ D d0 f C d 0f z f
ln r 0 z
(6)
and
ln Im .z/ D d0m C dm0 z m
ln 1
r 0z
(7)
The entire model consists of estimating equation (1) for each good k D 1,...,K using data from
widows, equation (2) for each good k, using data from widowers, and equation (5) for each good
k using data from married couples. All these equations need to be estimated simultaneously, both
because the errors " kf , "km , and "kh , will in general be correlated across goods k, and because many
of the same parameters appear in multiple equations.
As described earlier, our sample is restricted to married couples and widows/widowers between
the ages of 50 and 80, and we consider K D 9 expenditure categories: groceries, restaurant meals,
gasoline, personal care, clothing, vacation, utilities, garden supplies and services, car maintenance,
and housing (home repairs, supplies and services). The characteristics z that we include in the
model are age minus 60, self reported health status, retirement status, and education.
The data are constructed so that z D 0 in the benchmark speci cation corresponds to a couple
with a mean female income contribution and in which both spouses are still working, in good
health, and 60 years old. As a result, in our tables the reported value of r0 will equal the resource
share
for this group, and similarly for other subscript zero coef cients.
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5 Results
The estimation results for four speci cations of the model are presented in Table 5 and Table 6.
The joint system we estimate consists of the vectors of budget shares for widows, for widowers,
and for couples. For ef ciency, these are all estimated simultaneously, since all the parameters in
the widow and widower models also appear in the couple model. We estimate the joint system by
nonlinear seemingly unrelated regression.
Our benchmark speci cation, which allows both scale economies and the sharing rule to vary
with age and the health and retirement status of each spouse, is presented in Column 1. To measure
how allocation of resources among household members is affected by the amount each spouse
contributes to the household income, the sharing rule further includes the percentage of household
income that is earned by the wife. For comparison purposes, the speci cation in Column 2 allows
both scale economies and the sharing rule to vary with education instead of age of each spouse.
In Column 3 we report estimates of the benchmark model including data on all singles, not just
widows and widowers. Finally, Column 4 contains estimates of a version of the benchmark model
where the budget share for medical expenditures is incorporated.
The scale economy parameters are expected to yield values of
f
and
m
that lie between one-
half (complete sharing) and one (no sharing). The scale economy for couples in which the husband
is still in the labor force and in good health is
m
D 0:76. In other words, the shadow price faced by
married couples is associated with a cost-of-living index which is 76% of the costs faced by single
men. When the husband is in poor health, the scale economy is 0.69. For wives, the corresponding
scale economies are 0.61 and 0.59. Consistent with Lewbel and Pendakur (2008), these estimates
show that men face smaller scale economies than women, that is, a lower fraction of what men
consume is shared with their spouse. We also nd that for men and women, the estimated scale
economies are higher for individuals in poor health.
The estimated resource shares are comparably small. The wife's share of household consumption is 33% in a couple with a mean female income contribution and in which both spouses are still
working, in good health, and 60 years old. The resource shares also appear to be quite sensitive to
the health status of the husband. When her husband is in poor health, the wife's share rises to 48%.
In contrast to these health effects of the husband, resource shares seem largely unaffected by the
12
wife's health status, and by the retirement status of either spouse. The contribution of women to
household income raises her share signi cantly, while the age of both spouses affects their sharing
rule negatively.
The resource shares we nd for married women are smaller than those typically reported in
the literature. For example, Lewbel and Pendakur (2008) report wives' resource shares of between
0:36 and 0:46 using the same estimation method. Lise and Seitz (2011) report resource shares
averaging of 40%, while others report estimates near 0:5 (e.g., Cherchye, De Rock and Vermeulen,
2008) and higher (Browning, Chiappori, and Lewbel, 2004). These other paper's focus on working
age populations, so it is possible that women in our older households receive lower shares, perhaps
revealing a decrease in bargaining power with age.
The speci cation in Column 2 allows both scale economies and the sharing rule to vary with education (dummy variable for college educated or not) instead of age of each spouse. The estimated
resource share in a couple with a mean female income contribution and in which both spouses are
still working, in good health, and 60 years old is similar to the benchmark. The economies of scale,
however, are slightly larger for both men and women relative to the benchmark. College education
lowers the scale economies of both spouses signi cantly. The sharing rule, on the other hand, does
not differ by education level.
Our base model was estimated using couples along with widows and widowers, but excludes
divorced and never married single men and women, because divorced and never married individuals could have preferences over goods that differ from those who chose to not marry or to end
marriages. As a robustness check and to evaluate the importance of selection into marriage, Column 3 includes data on all single individuals in the data, instead of just widows and widowers.
Differences between these estimates and the previous columns could arise due to differences in the
preferences of widows and widowers versus other single women and men, or because of ef ciency
gains resulting from the use of a larger sample. The estimated economies of scale for healthy men
(0.79) and healthy women (0.61) who are working and 60 years old are lower than in the benchmark speci cation. The other estimates seem quite stable relative to the benchmark. The resource
shares are smaller than in the benchmark speci cation: Wife's share of household income is 31%
in a couple with a mean female income contribution and in which both spouses are still working,
in good health and 60 years old. The female income contribution has a signi cantly positive effect
13
on wife's share. Furthermore, a wife's share is signi cantly increased by her husband's poor health
and decreased by her own poor health.
With an average of 19%, medical expenditures are a large part of an older household's budget. We therefore estimate a version of the model in which medical expenditures are included in
the vector of budget shares in estimation in Column 4 (we do not use this case as our benchmark
because medical expenditures suffer from measurement error issues associated with differences
between actual consumption versus expenditures on insurance and copayments for service). Including medical expenditures, the estimated wives' resource share in a couple with both spouses
working, in good health, and 60 years old is larger than the benchmark. However, the wife's
resource share is now signi cantly lower when she is in poor health or when her husband is retired. For women, a poor health status also has a signi cant effect on their scale economies. The
economies of scale for healthy men who are not yet retired and 60 years old are again smaller than
for women, and men's economies of scale are signi cantly smaller when they are retired or in poor
health. Other estimates are similar to the benchmark case.
6 Conclusions
We estimate the extent to which joint consumption of some goods reduces the costs of living
for older couples versus living alone. We also estimate the fraction of household resources that
are consumed by wives versus husbands, taking this jointness of some consumption into account.
We show how these numbers are affected by the health and retirement status of each household
member.
We nd that older wives typically consume between 30% and 42% of total household expenditures (taking joint consumption and sharing of goods into account). These shares are somewhat
lower than what other researchers using similar methodologies have reported for younger couples.
We nd these shares are not affected much by retirement decisions, but wives shares increase substantially, up to 48%, when the husband's health is poorer. This increase in shares is consistent with
the interpretation of resource shares as a measure of relative bargaining power within a household.
As for economies of scale to consumption, we nd that by sharing consumption with his wife,
husbands only need to spend 76 cents for every dollar they would spend while living alone to attain
14
the same indifference curve over goods. This drops to 69 cents for men in poor health. For wives,
the corresponding number is near 60 cents regardless of health. So while wives get less than half
of the couples's resources, each dollar they do get allows them to buy more of what they consume
(relative to having the same resources when single) than each dollar their husband gets. Essentially,
this means that shared goods comprise a higher fraction of wive's consumption than of husband's
consumption.
Dividing each household member's economies of scale measure by their resource shares yields
that person's indifference scale. So for example a wife having a .35 resource share and .6 cost
of living index has an indifference scale of .35/.6 = .58, meaning that this woman would require
58% of the household's income to attain the same standard living if she were living alone that she
attains as a member of the couple. In contrast, a healthy older man living alone would require 86%
(.65/.76 = .86) of a couple's total expenditures to attain the same standard of living he enjoys while
married. This difference between men and women is largely due to the husband consuming much
more of the household's resources than the wife, though that is partly offset by the wife's greater
bene t from sharing goods. These differences would be directly relevant for marriage bargaining
models that are based on each member's outside option.
One useful area for future research would be incorporating time use into the model, because
time use is a substitute for some forms of consumption (e.g., home cooking versus purchase of prepared foods) and a complement to others (e.g., vacations), and because availability and allocation
of time use can be dramatically affected by changes in health and retirement status of both oneself
and one's spouse.
A second useful extension would be to nest this paper's model into a dynamic context, to permit
analysis of the timing of allocation issues, and the role of consumption smoothing over the latter
part of the life cycle. The types of intrahousehold allocations we identify could also be relevant for
determining the savings levels each household member, and likely impacts the timing of retirement
decisions.
15
7 References
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Becker, G.S. (1965): “A Theory of the Allocation of Time,” Economic Journal, 75, 493-517.
Becker G.S. (1981): “A Treatise on the Familiy,” Cambridge, Mass.: Harvard University Press.
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Blau, D. and D. Gilleskie (2006): “Health insurance and retirement of married couples,” Journal of Applied Econometrics, 21, 935-953.
Blundell, R., A. Duncan, and K. Pendakur (1998): “Semiparametric estimation and consumer
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Bourguignon, F., M. Browning, P.-A. Chiappori, and V. Lechene (1994): “Incomes and outcomes: a structural model of intra-household allocation,” Journal of Political Economy, 102, 10671096.
Bourguignon, F. and P.-A. Chiappori (1994): “The collective approach to household behaviour,” in The Measurement of Household Welfare, R.W. Blundell, I. Preston, and I. Walker, eds.,
70-85, Cambridge University Press.
Browning, M. and P.-A. Chiappori (1998): “Ef cient intra-household allocation: a characterisation and test,” Econometrica, 66, 1241-1278.
Browning, M., P.-A. Chiappori, and A. Lewbel (2004): “Estimating Consumption Economies
of Scale, Adult Equivalence Scales, and Household Bargaining Power,” Boston College Working
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Cherchye, L., B. De Rock, and F. Vermeulen (2008): “Economic well-being and poverty among
16
the elderly: An analysis based on a collective consumption model,” IZA Discussion Papers 3349.
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French, E. and J. Jones (2004): “The effects of health insurance and self-insurance on retirement behavior,” Center for Retirement Research Working Paper, 2004-12, Boston College.
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17
Table 1: Sample Statistics by Marital Status, 2005 and
2007 Waves of HRS/CAMS
Widowed
Widowed
Single
Single
Married
Married
Men
Women
Men
Women
Men
Women
68.9
68.8
64.5
65.9
66.7
63.7
(5.74)
(6.89)
(7.61)
(7.81)
(6.87)
(7.06)
High school
0.346
0.429
0.357
0.300
0.315
0.363
Some college
0.212
0.244
0.343
0.320
0.240
0.284
College
0.261
0.130
0.224
0.262
0.364
0.286
Good health
0.729
0.779
0.718
0.699
0.857
0.870
Retired
0.529
0.478
0.335
0.258
0.457
0.258
Age
Female income contribution
0.337
(0.261)
Observations
79
420
Notes: Mean and standard errors in parentheses.
18
223
387
1004
1004
Table 2: Budget Shares by Marital Status, 2005 and
2007 Waves of HRS/CAMS
Widowed
Widowed
Single
Single
Married
Men
Women
Men
Women
Couples
Groceries
0.227
0.218
0.201
0.206
0.225
Restaurant
0.090
0.056
0.107
0.059
0.087
Gasoline
0.107
0.067
0.117
0.079
0.111
Personal care
0.018
0.041
0.025
0.042
0.034
Clothing
0.031
0.051
0.037
0.063
0.048
Vacations
0.078
0.067
0.068
0.074
0.131
Utilities
0.256
0.285
0.250
0.282
0.155
Gardening
0.016
0.043
0.023
0.032
0.032
Car Maintenance
0.034
0.038
0.048
0.042
0.040
Home Maintenance
0.143
0.133
0.124
0.119
0.138
79
420
223
387
1004
Observations
19
Table 3: Budget Shares by Retirement Status for Married Couples, 2005 and 2007 Waves of HRS/CAMS
Husband
Husband
Wife
Wife
Not Retired
Retired
Not Retired
Retired
Groceries
0.212
0.240
0.223
0.230
Restaurant
0.093
0.081
0.088
0.086
Gasoline
0.122
0.097
0.118
0.090
Personal care
0.034
0.033
0.035
0.030
Clothing
0.051
0.044
0.049
0.044
Vacations
0.124
0.141
0.125
0.149
Utilities
0.152
0.159
0.159
0.145
Gardening
0.029
0.035
0.028
0.041
Car Maintenance
0.042
0.037
0.040
0.039
Home Maintenance
0.141
0.134
0.135
0.145
454
550
669
335
Observations
20
Table 4: Budget Shares by Health Status for Married
Couples, 2005 and 2007 Waves of HRS/CAMS
Husband in
Husband in
Good Health Poor Health
Wife in
Wife in
Good Health
Poor Health
Groceries
0.221
0.245
0.217
0.276
Restaurant
0.091
0.067
0.092
0.060
Gasoline
0.109
0.118
0.109
0.121
Personal care
0.033
0.038
0.034
0.033
Clothing
0.047
0.054
0.048
0.048
Vacations
0.135
0.111
0.141
0.069
Utilities
0.153
0.168
0.152
0.178
Gardening
0.031
0.034
0.032
0.029
Car Maintenance
0.040
0.038
0.039
0.047
Home Maintenance
0.139
0.127
0.137
0.139
839
165
863
141
Observations
21
Table 5: Estimation Results: Scale Economies
Controls for Age,
Controls for Education,
Include all
Medical
Health, and Retirement
Health, and Retirement
Singles
Expenditures
-0.281
-0.333
-0.239
-0.230
(0.010)
(0.035)
(0.007)
(0.059)
0.099
0.044
0.007
0.004
(0.043)
(0.017)
(0.002)
(0.001)
-0.086
-0.056
0.002
-0.023
(0.029)
(0.019)
(0.006)
(0.005)
0.068
-0.005
-0.013
(0.030)
(0.008)
(0.008)
Husband Scale Economy
Intercept
Retirement
Poor health
Age
Education
-0.087
(0.034)
Wife Scale Economy
Intercept
Retirement
Poor health
Age
-0.497
-0.564
-0.371
-0.501
(0.175)
(0.185)
(0.123)
(0.136)
-0.019
-0.210
0.005
0.073
(0.010)
(0.098)
(0.003)
(0.376)
-0.031
-0.063
0.076
0.002
(0.016)
(0.029)
(0.019)
(0.001)
0.037
0.086
-0.048
(0.012)
(0.137)
(0.027)
Education
-0.087
(0.022)
Observations
1503
1503
2113
1503
# of coef cients
132
132
132
144
22
Table 6: Estimation Results: Resource Shares
Intercept
Income share of wife
Husband retired
Wife retired
Husband in poor health
Wife in poor health
Husband's age
Wife's age
Controls for Age,
Controls for Education,
Include all
Medical
Health, and Retirement
Health, and Retirement
Singles
Expenditures
0.333
0.342
0.306
0.412
(0.035)
(0.037)
(0.078)
(0.117)
0.004
0.004
0.008
0.0008
(0.001)
(0.002)
(0.003)
(0.0005)
0.018
-0.069
-0.0002
-0.031
(0.027)
(0.028)
(0.0002)
(0.008)
0.0005
0.030
0.0001
-0.016
(0.029)
(0.016)
(0.0001)
(0.034)
0.143
0.027
0.013
0.126
(0.052)
(0.021)
(0.003)
(0.069)
-0.046
-0.083
-0.032
-0.175
(0.042)
(0.033)
(0.010)
(0.055)
-0.007
-0.004
-0.001
(0.002)
(0.003)
(0.002)
-0.008
-0.003
-0.001
(0.002)
(0.003)
(0.003)
Husband's education
0.002
(0.008)
Wife's education
0.002
(0.008)
Observations
1503
1503
2113
1503
# of coef cients
132
132
132
144
23